Because of the properties such as high specific strength and stiffness, high chemical resistance, and low thermal expansion, carbon fiber has been used widely in aerospace, sports, and commercial industries of automobile, wind energy, and other energy saving areas. Typically, carbon fibers are made from polyacrylonitrile (PAN)-based polymers.
Free Radical Polymerization
PAN polymers, traditionally, are made by free radical polymerization method. In free radical polymerization, a catalyst or an initiator initiates first to form initial free-radical species. These radical species start to react with monomers to create active centers to form free monomer-radicals. Then the monomer radicals react with other monomers to propagate the molecular chain to form polymer radicals.
During the polymerization, sometimes, one radical reacts with other radical to couple and form a long dead chain, as a combination termination, while some radical at the end of one chain may attack a hydrogen atom at the second-to-last carbon atom in the second radical chain to form a dis-proportionation termination. The polymer radical can also react with another compound, such as a chain transfer agent, to terminate the propagation reaction of the polymer radical, and to form a new radical from chain transfer agent. This newly formed chain transfer radical starts its new chain propagation. Thus, the chain transfer agent reduces the length of polymer radical chain grown. If the rate of this termination is much higher than the rate of propagation, then very small polymers with short chain lengths are formed. Therefore, the chain transfer agent is used to control the molecular length or weight of the polymer. Because of the different termination mechanisms, the resulting molecular chains have different lengths or different molecular weights. As such, the molecular weight of polymers has a distribution. This distribution can be defined by its polydispersity index (PDI), as follows:
  PDI  =            Mw      ⁢                          ⁢              (                  Weight          ⁢                                          ⁢          average          ⁢                                          ⁢          molecular          ⁢                                          ⁢          weight                )                    Mn      ⁢                          ⁢              (                  number          ⁢                                          ⁢          average          ⁢                                          ⁢          molecular          ⁢                                          ⁢          weigh                )            Alternatively, PDI may be expressed as follows:
  PDI  =            Mz      ⁢                          ⁢              (                  Z          ⁢                      -                    ⁢          average          ⁢                                          ⁢          molecular          ⁢                                          ⁢          weight                )                    Mw      ⁢                          ⁢              (                  weight          ⁢                                          ⁢          average          ⁢                                          ⁢          molecular          ⁢                                          ⁢          weight                )            Mw, Mn, Mz are measured by a GPC (gel permeation chromatography) method. Here, Mw is the weight average molecular weight. Mn is the number average molecular weight and Mz is the Z-average molecular weight or the size average molecular weight.
A high PDI indicates that the polymer has a large molecular weight distribution, which means the polymer has very high molecular weight species or very low molecular weight species, or both. In other words, the polymer is composed of molecular chains that vary greatly in lengths. The presence of too high molecular weight or too small molecular weight species will affect the process-ability of the polymer into fibers by spinning and the resulting fiber properties, especially the too small molecular weight species, due to the fact that the small molecular weight species are a kind of molecular defect to polymer mechanical properties.
PAN polymer prepared by conventional radical polymerization does not allow control over polymerization. The resulting polymer has large molecular weight distribution. Thus, there is a difficulty for the mechanical property development of the fibers spun from such PAN.